Question

Solve the equation using quadratic formula.

$4a^2-3a+8=0$

Short answer

No real solutions.

The discriminant is less than zero or negative, the quadratic equation cannot have real solutions.

Step-by-step solution

 Given Information.   

The given equation is$4a^2-3a+8=0$.

Write the quadratic equation in standard form and identify a,b,c.

The quadratic equation is in standard form.

So,

$a=4,b=-3,c=8$.

Substitute the values in quadratic formula.   

$$\begin{gathered} a=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ a=\frac{-(-3)\pm \sqrt{(-3{)}^2-4(4\left)\right(8)}}{2\left(4\right)} \\ a=\frac{3\pm \sqrt{9-128}}{8} \\ a=\frac{3\pm \sqrt{-119}}{8} \end{gathered}$$

Since $\sqrt{-119}$is not a real number, or we can say that the discriminant is less than zero.

The equation has no real solutions.